You seem to have a very tight window for your cruise. I’ve trawled the high seas of the Internet and can find exactly one Baltic cruise that fits your requirements of not more than seven days long and between September 5 and 14. And that’s MSC Cruises’ ‘7 night Northern Europe Cruise’ on the MSC Splendida. This cruise offers a range of departures in September, including one on September 7, which seems to be the only one within range. The port of departure is Southampton, and the cruise then moves to Zeebrugge (Belgium), Amsterdam (Netherlands), Hamburg (Germany), Le Havre (France), and then back to Southampton. Prices for this particular cruise start at US$869 per person for an inside stateroom. (The September 14 departure is priced much lower, starting at $599 per person, but unfortunately doesn’t fit your dates.) See www.msccruises.com.
I can also find only one Mediterranean cruise that might fit your dates. If you have any kind of flexibility on your budget, you might want to consider P&O Cruises’ ‘7 Night Mediterranean Cruise’, which is a mid-sized ship that won’t be too overwhelming for first-timers and is an adults-only vessel catering to a more mature group. This cruise begins in Genoa (Italy), moving to Florence/Pisa (Italy), Naples (Italy), Dubrovnik (Croatia) and finally Venice (Italy). This is a ‘fly cruise’, meaning the price includes flights from London Gatwick and back; prices start from P799 per person. See www.pocruises.com.
I’m afraid a UK visa will not work for any other country in Europe. Though still in the EU at the time of going to press, this is an embattled business, of course; and the UK visa holds good only for the UK. You will need a Schengen visa to enter any other European country. Once you decide on your cruise, and know your first port of call (outside the UK), you will have to apply for a multiple-entry Schengen visa from that country. So, if Zeebrugge is your first stop, apply for a Schengen visa at the Embassy of Belgium; if Genoa, then the Embassy of Italy and so on. A multiple-entry visa is crucial too!